Solvent flux

Reviews of concentration polarization have been reported (14,38,39). Because solute wall concentration may not be experimentally measurable, models relating solute and solvent fluxes to hydrodynamic parameters are needed for system design. The Navier-Stokes diffusion—convection equation has been numerically solved to calculate wall concentration, and thus the water flux and permeate quaUty (40). 

Osmotic Pinch As the feed travels along the feed channels, friction losses lower the feed pressure. Solvent flux along the feed channel dewaters the feed and increases solute concentration and osmotic pressure. For a recovery or conversion ratio CR, a module solute retention R, and an inlet solute concentration of c , the bulk concentration cj, is... 

It is an empirical fact that in the absence of a significant exchange Of solvent flux with the vapor phase the position of the solvent front with respect to time is adequately represented by... 

Since the ionic fluxes cannot be measured individually, it is preferable to introduce the salt flux, besides solvent flux and charge flux (current density). The driving forces would then be the gradients or differences of the chemical potentials in media with different salt concentrations and different pressures, multiplied by -1. These differences must be relatively small to remain within the framework of linear irreversible thermodynamics, so that... 

Solvent flux Salt rejection Recovery Feed-temp. 

Solvent flux (gfd) Salt rejection % Recovery % Remarks... 

Solids such as KF, PbO, PbFj and BjOj are powerful solvents (flux) in the molten state for many inorganic substances and hence can be used as media for the growth of crystals. The usual technique is to dissolve the solute in a suitable combination of flux... 

COPPER-SOLVENT FLUX GROWTH OF MANGANESE MONOSILICIDE... 

Copper-Solvent Flux Growth of Manganese Monostticide 183... 

The solvent flux across the membrane / is proportional to the applied force, which is equal to the applied pressure reduced by the osmotic pressure All as (Belter et al., p. 255,1988),... 

The flux of solute from the bulk of the solution to the membrane surface is equal to the solute concentration times solvent flux CJ. At steady state, it will be countered by the molecular diffusion of the solute away from the membrane surface as... 

The decrease of the solution volume is equal to the membrane area A times the solvent flux across the membrane f. 

The development of the first transdermal patches in the 1980s generated considerable interest in this route of drug administration. Soon afterwards, iontophoresis was rediscovered and its potential to contribute to the new field of transdermal drug delivery was examined. This work provided the basic principles for modern iontophoretic devices [13,18-21]. Furthermore, and importantly, they demonstrated the existence of a (primarily) electroosmotic, convective solvent flux during transdermal iontophoresis [10,11,22-24], and it was shown that the permselective properties of the skin (a) could be exploited to enhance the transport of neutral, polar species and (b) have a clear impact on ionic transport. Subsequent research has better characterized skin permselectivity and the factors which determine the magnitude of electroosmosis [25-27],... 

The mathematical description of this process is identical to that of reverse osmosis given in Equations (2.37) and (2.44) and leads to expressions for the solute and solvent fluxes... 

The results illustrated in Figure 2.16 show that the solvent flux tends towards a limiting value at very high pressures. This value is reached when the concentration of sorbed solvent at the permeate side of the membrane reaches zero, the limiting value. 

D.R. Machado, D. Hasson and R. Semiat, Effect of Solvent Properties on Permeate Flow Through Nanofiltration Membranes. Part I Investigation of Parameters Affecting Solvent Flux, J. Membr. Sci. 163, 93 (1999). 

Figure 5. Navier-Stokes flow through a slit solvent flux for (a) uncharged species and (b) charged species.

The permeability Ps is a measure of the transport of a molecule by diffusion. The reflection coefficient a of a given component is the maximal possible rejection for that component (at infinite solvent flux). Various models have been proposed for the reflection coefficient [75-77]. In the lognormal model [78], a lognormal distribution is assumed for the pore size. No steric hindrance in the pores or hydrodynamic lag is taken into account, but it is assumed that a molecule permeates through every pore that is larger than the diameter of the molecule. Moreover, the diffusion contribution to the transport through the membrane is considered to be negligible. Therefore, the reflection curve can be expressed as ... 

Mass-transport limitations are common to all processes involving mass transfer at interfaces, and membranes are not an exception. This problem can be extremely important both for situations where the transport of solvent through the membrane is faster and preferential when compared with the transport of solute(s) - which happens with membrane filtration processes such as microfiltration and ultrafiltration - as well as with processes where the flux of solute(s) is preferential, as happens in organophilic pervaporation. In the first case, the concentration of solute builds up near the membrane interface, while in the second case a depletion of solute occurs. In both situations the performance of the system is affected negatively (1) solute accumulation leads, ultimately, to a loss of selectivity for solute rejection, promotes conditions for membrane fouling and local increase of osmotic pressure difference, which impacts on solvent flux (2) solute depletion at the membrane surface diminishes the driving force for solute transport, which impacts on solute flux and, ultimately, on the overall process selectivity towards the transport of that specific solute. 

In the absence of suspended solutes or colloids, the pure solvent flux through an ultrafiltration membrane is directly proportional to the applied pressure difference and inversely proportional to the viscosity of the solvent and the membrane thickness. Transport within the pores occurs in the creeping flow regime, since kinematic viscosities of liquids are sufficient to make Re < C 1 for practical pore sizes. In the simplest case, the membrane can be considered to be a packed array of straight, equal diameter nonintersecting capillary tubes. The observed volumetric flux, nAvA (cc/sec cm2), equals the product of the mass flux of solvent based on the total membrane area, nA... 

Solvent flux is given by Equation 4.1, where transport is proportional to the pressure driving force. The total solute flux depends on diffusion and is given by Equation 4.5 ... 

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